Ordering and criticality in an underscreened Kondo chain

Motivated by the nickel valence controversy in the perovskite nickelate RNiO_3, we consider a one-dimensional underscreened Kondo chain consisting of alternating spin-1 ("nickel") and electron ("oxygen") sites, which in addition to the usual electron hopping and spin-spin interaction between the S=1 spin and the electron also contains a spin mediated electron hopping term. Using the density-matrix renormalization group (DMRG), we obtained the zero temperature phase diagram of the model, as well as various correlation functions in each phase. Importantly, for a certain range of parameters the model exhibits a quasi-long-range spiral (QS) order. To understand the DMRG results, we construct a mean-field theory based on a Schwinger fermion decomposition of the S=1 spins, from which we argue that the QS phase corresponds to a phase in proximity to the spin Bose metal state proposed by D. N. Sheng, O. I. Motrunich, and M. P. A. Fisher [Phys. Rev. B 79, 205112 (2009)]. Notably, we find no evidence for a phase with the symmetry of "nickel"-centered charge order, which has been argued to arise due to site-selective Kondo screening of half the S=1 spins, and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions, not present in this model.